Timelineof Structural Theory

In large part the science of chemistry is concerned with modelling the chemical
structure of matter and understanding the nature of the chemical bond. However,
the chemical bond sits right on the boundary between the classical
and quantum mechanical worlds and academics, professional chemists and teachers
liberally pick ideas, concepts and models from both. To understand the nature
of chemical bonding it is necessary to see how the various ideas have developed
over the past 200 years. This page introduces the main theoretical approaches
to understanding chemical structure and reactivity, places them in historical
context and considers them with reference to each other.

Introduction

When chemists think about the
structure and behaviour of a substance like ammonia, NH3,
they are influenced by experimental (empirical) evidence, physical theory,
the history of science, educational dogma and philosophical position.

There are three general approaches
to understanding a substance such as ammonia, NH3:

Empirical
study is concerned with observation
and experiment rather than explanation and theory,
but theory may guide experiment and experiments often lead to the development
of new theory.

Chemistry sits right on the
boundary between the quantum and classical worlds: the chemical bond is
a quantum mechanical construct but the behaviour of molecular entities
can often and conveniently be described in classical terms. As a result
we have two entirely different types of model of chemical structure, bonding
and reactivity.

On one hand, we
have theories that treat electrons as countable dots and stress the
importance of electron accountancy. These "Lewis" models recognise
 but cannot explain  the magic numbers of electrons associated
with the group 18 elements (He, Ne, Ar, Kr, Xe), aromatic π-systems,
18-electron transition metal complexes, etc. Models include: Lewis octet
theory, Lewis acids/base theory, electron accountancy, reactions mechanisms
& curly arrows, VSEPR, molecular mechanics, etc. While the various
Lewis electron accountancy models work most of the time, they do not
work all the time. Lewis theory cannot explain atomic or molecular spectroscopy
or why oxygen, O2, is paramagnetic.

On the other hand,
we have quantum theory and models derived from the Schrödinger
wave equation. These wave mechanical approaches lead to atomic orbitals,
molecular orbital theory, valence bond theory and FMO theory. The MO
approach has been developed into software such as Gaussian
and Spartan. Quantum chemistry
techniques give good numerical answers, but they are conceptually difficult.

Students tend to
be introduced to chemistry through the various Lewis models... and are
then surprised to learn they that these models are not the whole story
and can even be wrong.

The diagram below shows a timeline
of the development of the main theoretical chemical structure and reactivity
ideas over the last 200 years:

The red arrows in the diagram are used
to represent the act of "conversion from quantum to classical".
They are used twice, between the Bohr atom and Lewis theory, and between
VB theory and VSEPR theory. On
both occasions there is a theoretical leap of faith because the
impression is given that Lewis theory and VSEPR theory are based upon
quantum theory, when they are not.

Timelines: A Proviso

One reader of this page has pointed out that the irresistible temptation to show the logical development of a subject using timelines does not represent the actual history, which is never neat & tidy.

1803:John Daltonargued
 on the 21st of October 1803 to the Manchester Literary and Philosophical
Society in Manchester, and I am writing this text on the 200th anniversary
and less than a mile away  for the atomic theory originally
proposed by the Greeks. Dalton defined an atom as the smallest part of
a substance that can participate in a chemical reaction. He proposed that
elements are composed of identical atoms and that elements combine in
definite proportions, stoichiometry. Dalton also produced an early
table of atomic weights.

1869: The Mendeleev Tablelle
I, the first plausible periodic table, was published. It was constructed
using the recently discovered element, stoichiometric and periodicity
data because some 35 elements had been discovered since 1800.

The success of this first version
can be attributed to the gaps which Mendeleev correctly predicted would
contain undiscovered elements, and he predicted their properties.

To the modern eye, the biggest
omissions are the the Group 18 rare gases (He, Ne, Ar, K & Xe) and
that only a small number of f-block elements are shown.

Of more importance, however,
is that the elements are arranged by mass rather than atomic number, a
concept had yet to be discovered so Mendeleev can be forgiven.

In the year 1904, JJ Thomson proposed that the atom had a "plum pudding" structure, with the negative electrons
in circular arrays – the plums – embedded in a spherical pudding
of positive charge with mass evenly distributed. It was the study of radioactivity,
in particular alpha radiation, that enabled Rutherford to develop his
experiments to probe atomic structure.

March 1904 edition of the Philosophical Magazine JJ Thomson writes: "... the atoms of the elements consist of a number of negatively electrified corpuscles enclosed in a sphere of uniform positive electrification, ..."

Diagram from Wikipedia & Charles Baily's presentation: here. The lower depictions are incorrect, in the sense that they are not true to the model proposed by Thompson in 1904.

1905: Einstein and the Photoelectric
Effect It was known from experiment that metals emit electrons
when exposed to light (the system has to be in a vacuum), however, it
could not be explained why the rate of emission depended upon the wavelength
of the light in the way that it did. In 1905, Einstein showed that if
light consisted of particle-like quantised photons, where the energy
of the photon depended upon its wavelength, the photoelectric effect could
be explained. This work led to a revolution in the understanding of both
the electron and light. Light could behave as both a wave and a particle,
depending upon the experiment. It was for this work that Einstein received
the Nobel prize.

1911:Rutherford,
already a Nobel prize winner (1908), interpreted the results of the Geiger-Marsden
experiment involving a beam of alpha particles fired at a thin foil
of gold designed to measure the deflection as the alpha particles interacted
with the "plum-pudding" gold atoms.

Rutherford was astonished with
the results which showed that most of the alpha particles passed straight
through the gold foil unaffected, but a small minority were deflected
by large angles. Rutherford commented at the result: "It was almost
as incredible as if you fired a fifteen-inch shell at a piece of tissue
paper and it came back and hit you".

Rutherford proposed a model
of the atom had a very small, dense, positively charged nucleus surrounded
by electrons.

The HyperPhysics website has a nice diagram comparing the tiny size of the nucleus and the size of a gold atom with the sizes of the Sun and the solar system. This is our version of the diagram, converted to metric units:

The "Rutherford Atom" has developed into a model that is still widely used, although the artists impressions hugely distort the relative sizes of the various atomic components (much to this author's annoyance!):

Our story now moves on from atomic structure to how the negative electrons 'associate' with positive nucleus.

1913: The
Bohr Atom In 1913 Niels Bohr - while working in Rutherford's laboratory
- constructed a model of the atom that had small, light, fast, particle-like,
negatively charged electrons "orbiting" a small, massive positively charged
nucleus... although the reason why the electron did not spiral into the
nucleus could not be explained. The electron shells were quantised, and
as the electrons moved from shell to shell they emitted or absorbed photons
the energy of which was equal to the energy difference between the shells.

The Bohr model is the first
plausible model of the atom and it is still widely used in education,
particularly in illustrations because it is so easy to draw and understand.

Diagram from Wikipedia: "The Rutherford-Bohr model of the hydrogen atom (Z = 1) or a hydrogen-like ion (Z > 1), where the negatively charged electron confined to an atomic shell encircles a small positively charged atomic nucleus, and an electron jump between orbits is accompanied by an emitted or absorbed amount of electromagnetic energy (hν). The orbits that the electron may travel in are shown as grey circles; their radius increases as n2, where n is the principal quantum number. The 3 → 2 transition depicted here produces the first line of the Balmer series, and for hydrogen (Z = 1) results in a photon of wavelength 656 nm (red)."

Atomic Modeling in the Early 20th Century: 1904-1913

Charles Baily, University of Colorado, Boulder

This excellent Power Point presentation – now as a .pdf file – discusses:

J.J. Thomson (1904): “Plum Pudding” Model

Hantaro Nagaoka (1904): “Saturnian” Model

Ernest Rutherford (1911): Nuclear Model

Niels Bohr (1913): Quantum Model

Personal communication: There is an associated paper by Charles Baily with the same title presented at the 24th Regional Conference on the History and Philosophy of Science, Boulder, CO (10/12/08).

1916:Lewis
Theory was developed at UC Berkeley
by the active research group led by G.N.Lewis. The theory was first published
in 1916
and was expanded in book form 1923.

Lewis used the new ideas about
atomic structure that were widely discussed in his labs:

atomic number

Bohr atom

developing periodic
table

crucial importance
of the electron

chemistry of ionic
solutions

molecular structure

etc.

Lewis proposed the two electron
chemical bond, later named the covalent bond by Langmuir. Linus
Pauling supported the Lewis analysis, here.

Students of chemistry first
learn about Lewis through the well known (some would say too
well known) Lewis Octet Rule. This extraordinarily useful
rule of thumb states that atoms like to have a full octet of eight electrons
in their outer or valence shell. The argument is that fluorine, with
seven electrons 'wants' another electron to give the stable 'full octet'
fluorine ion, F. Likewise, sodium loses an electron
to give the sodium ion, Na+, another species with a full
octet. Students soon
realise that 8 is not the only special number. Phosphorus pentachloride,
PCl5, has 10 electrons. Benzene has 6 electrons
in its aromatic π-system. Transition metal
complexes often follow the 18 electron rule. Etc.

The Lewis model in its modern
form is widely taught in schools and at university level, even though
Lewis's electrons are entirely classical:

Negative electron dots
are simply assigned to atomic shells, covalent bonds or lone pairs,
where they are counted against positive nuclear charge.

The 'theory' gives absolutely
no explanation as to why the numbers of electrons about an atomic centre:
2, 8, 8, 18, 18, 32, should exhibit such special stability.

Yet, Lewis theory and
electron accountancy are the key tools used by most chemists most
of the time to help understand structure and reactivity.

Some examples of Lewis theory
in action:

Lewis theory that
it can be superimposed upon Mendeleevs Periodic Table where it
explains vast amounts of structural and reaction chemistry:

Lewis theory can
be used to describe and explain the reaction between lithium and fluorine
to give lithium fluoride, where the Li+ ion is isoelectronic
with He and F is isoelectronic with Ne:

Lewis theory can
be used to describe and explain the molecular structure of a substance
methane, CH4. The Lewis argument is that carbon has 4 electrons in its
valence shell, and four hydrogens each with one electron in their valence
shell. These
combine to give CH4 in which electrons are shared
between atoms. In the Lewis structure, each hydrogen has two electrons
in its valence shell, and the carbon eight. The Lewis structure maps
straight onto the VSEPR (AX4) structure:

Lewis theory, electron
accountancy and magic numbers can be used to describe and explain the
structure and reactivity of many reactive species, including Lewis acids
and Lewis bases such as borane, BH3, and ammonia,
NH3. Borane,
BH3, has only six electrons in its valence shell,
but it wants eight and it is an electron pair acceptor. Ammonia,
NH3, has a full octet, but two of the electrons
present as a reactive lone-pair. Borane reacts with ammonia to form
a Lewis acid/base complex in which both the boron and the nitrogen atoms
no have a full octet. No explanation is given within Lewis theory
as to why the number eight should be so important:

Lewis theory, electron
accountancy and magic numbers are used to explain most types of reaction
mechanisms, including Lewis acid/base, redox reactions, radical, diradical
and photochemical reactions. Whenever a curly arrow is used in a reaction
mechanism, Lewis theory is being evoked. Do not be fooled by the sparse
structural representations employed by organic chemists, curly arrows
and inter converting resonance structures are pure Lewis theory:

Valence Shell Electron Pair
Repulsion, below and in detail here,
is an extension of Lewis theory.

Lewis theory is very
accommodating and is able to 'add-on' those bits of chemical structure
and reactivity that it is not very good at explaining itself. Consider
the mechanism of electrophilic aromatic substitution, SEAr:

The diagram above
is pure Lewis theory:

The toluene is
assumed to have a sigma-skeleton that can be described with VSEPR.

The benzene π-system
is added to the sigma-skeleton, but it is really a Lewis construct
when described as "planar, cyclic and containing six π-electrons".
Six is a magic number.

The curly arrows
are showing the movement of pairs of electrons, pure Lewis.

The Wheland intermediate
is deemed to be non-aromatic because it does not possess the magic
number six π-electrons.

In Lewis theory, benzene's
six π-electrons
have exactly the same status as neon's eight electrons. Both are magic
numbers associated with stability, but no explanation is given as to why
this should be so.

Lewis
theory is bad at explaining:

The nature of the
covalent bond
Why oxygen, O2, is a magnetic
diradical
The hydrogen
bridge bond found in diborane, B2H6π-systems
Transition metal chemistry

Read more about Lewis structures
and the relationship between Lewis theory and other structural theories
in an excellent
page by physicist John Denker.

1913-25: Spectroscopy &
Quantum Numbers Atomic spectra had been taken since the 1850s by scientists like Bunsen and Kirchhoff. In Denmark, Niels Bohr re-studied atomic spectra and
- along with Sommerfield, Stoner and Pauli - devised the quantum numbers
from empirical (spectroscopic) evidence:

After the discovery/invention
of the Schrödinger wave equation, below, the Bohr model became known
as the old quantum theory, here
and Wikipedia.

Question: Is
light made of waves or particles?

Answer: Both

Experiments
that explore the wave-nature of light show light to be wavelike...
and experiments that demonstrate that light is made of discrete
photons show that light is indeed constructed from particles.

Weird.

Yeah, we know.
Just get used to it. Light is said to exhibit 'wave-particle
duality'.

In 1924 de
Broglie's proposed that all moving particles has a wavelength
is inversely proportional to momentum and that the frequency is
directly proportional to the particle's kinetic energy (Wikipedia):

λ = h/p

This concept
leads to one of the most important ideas in 20th century science:

The small,
light, fast moving electron also exhibits wave-particle duality.
It can be conceived of as a particle or as a wave.

Edwin Schrödinger knew
of de Broglie's proposal that a electrons exhibited wave-particle duality.
With this idea in mind,
he devised/constructed a differential equation for a wavelike electron
resonating in three dimensions about a point positive charge.

Solutions to the Schrödinger
wave equation - resonance modes described by mathematical wavefunctions
- assumed discrete, quantised, energies which corresponded to spectral
lines of one electron atoms and ions: H, He+, Li2+
etc., and they corresponded exactly with Bohr's quantum
numbers. This development lead to quantum mechanics.

Waves and the the mathematical
functions that describe them: wavefunctions, are well understood
mathematically. For example, they can be added together or subtracted
from each other. Consider two sine waves and their superposition,
here:

The atomic orbitals derived
from the Schrödinger wave equation, being waves, can be added together.
The arithmetic can be carried out in various ways.

The term "wavefunction"
can be interchanged with term "orbital". By convention, mathematical
expressions are termed wavefunctions and chemical structure and
structure and reactivity are discussed with reference to orbitals.

Atomic Orbitals are
constructed from the four quantum numbers.
The AOs fill with electrons, lowest energy AO first, the aufbau principle.
An orbital can contain a maximum of two electrons, and these must be of
opposite spin, the Pauli exclusion principle. One final rule, Madelung's
rule points out that the orbitals fill with electrons as n +
l, as principle quantum number plus subsidiary quantum number, rather
than n.

Orbitals shape
and phase. s-Orbitals are radial and they have n-1 (n minus one) nodes,
where n is the principal quantum number. Thus, the 1s orbital is devoid
of nodes, the 2s orbital has one node, etc. The s-orbital nodes are spherical
and they are best viewed in cross section (below). There is a change of
phase at the node. Max Born suggested that the squared wavefunction equates
electron density, but squaring results in the loss of all phase information.

p-Orbitals have both radial
and angular components and have a "figure of 8" shape.

1928: Pauling's Five Rules:
Crystal Structure

The crystal structure of an
ionic compound can be predicted using a set of empirical rules:

The First Rule:
Around every cation, a coordination polyhedron of anions forms, in which
the cation-anion distance is determined by the radius sums and the coordination
number is determined by the radius ratio.

The Number of Polyhedra
with a Common Corner - The Electrostatic Valence Rule: An ionic structure
will be stable to the extent that the sum of the strengths of the electrostatic
bonds that reach an anion equals the charge on that anion.

The Sharing of
Polyhedra Edges, Faces & Corners, particularly faces by two anion
polyhedra, decreases the stability of a crystal.

An extension of
the third rule: In a crystal which contains different cations, those
with high charge and low coordination numbers tend not to share elements
of their coordination polyhedra.

The Rule of Parsimony
The number of essentially different kinds of constituents in a crystal
tends to be small.

1932: Pauling's Electronegativity
Linus Pauling used empirical heat of reaction data to introduce the elemental
property of electronegativity which he defined as: "The desire
of an atom to attract electrons to itself".

Electronegative elements, such
as fluorine, "want" electrons so they can form negative ions
while electropositive elements, such as cesium, like to lose electrons
and form positive ions.

The great befit of electronegativity
is that the numbers can be used to quantify this effect and predict bond
dipole moment (polarity) and degree of ionic character. For example: fluorine
(3.98) is electronegative and cesium (0.79) electropositive. CsF is strongly
polarised Cs+ F and is 89% ionic.

1930: Valence
Bond Theory Once atomic orbitals were understood in terms
of both Bohr's quantum numbers and the Schrödinger wave equation,
the quest was on to understand bonding in molecules. Linus Pauling's approach
was to take the atomic orbitals and mix (hybridize) them together. For
example, the 2s orbital can mix with the three 2p orbitals to give four
"hybrid" sp3 orbitals which are arranged tetrahedrally about the central
atom.

Thus, hybridization can rather
easily explain the tetrahedral geometry of methane. Valence bond theory
can also explain why the carbons in ethene (ethylene) are triangular planar
by invoking sp2 hybridization and why ethyne (acetylene) is linear: sp
hybridization.

VB theory also introduces the
concept of "resonance", an idea dependent upon electronegativity. For
example, chlorine is more electronegative than hydrogen and the compound
hydrogen chloride, HCl, is polarised H+Cl.
VB theory suggests the various possible forms are in resonance.

VB theory is widely employed
in education because it produces easily understandable structures. However,
the mathematics of orbital manipulation is easier if non-hybridized orbitals
are employed. For this reason VB theory has become a theoretical "dead
end" compared with MO theory... or has it? Look here.

Read more about the valence
bond approach to understanding polyatomic structure here.

Molecular Orbital Theory
assumes that molecules are multi-nucleated atoms: the molecular orbitals,
MOs, are assumed to encompass the two nuclei. Electrons are added to the
MOs using the same rules that are used to add electrons to atomic orbitals:
the aufbau principle and the Pauli exclusion principle. MOs have a similar
geometry to atomic orbitals, but are more involved. The MO approach is
most obviously seen and understood with diatomic molecules, H2,
N2, etc.

The MO approach to diatomic
hydrogen places the two nuclei (protons) close to each other. An electron
is added to the lowest energy MO, the sigma bonding MO. The second electron
also goes into the sigma MO. The third electron goes into the next MO
which has a node between the two nuclei (a region of zero of electron
density) and is called the "sigma star" antibonding MO.

However, the all encompassing
MO approach is difficult to apply to molecules with many atoms. The 'trick'
is to use the Linear Combination of Atomic Orbital (LCAO) simplification
in which atomic orbitals are added together to form molecular orbitals.
Hydrogen is constructed by adding two 1s orbitals into a 1 sigma MO.

The interaction of atomic and
molecular orbitals can be represented in MO Energy diagrams:

There are various possible
AO to MO interactions:

The LCAO approach has been
highly developed in software. The AOs are described in terms of "basis
functions", such as finite elements, Gaussian type orbitals (GTOs)
or Slater type orbitals (STOs). (For historical reasons basis functions
are called basis AOs. Such ab initio (or "from the start")
software is able to
calculate molecular geometry and energy to high precision. Commercial
software is available.

The Hellmann-Feynman theorem
states that once the spatial distribution of electrons has been determined
by solving the Schrödinger equation, all the forces in the system
can be calculated using classical electrostatics.

Thus classically, the
equilibrium configuration of a molecule like H2,
(HH, bond length 74 pm) has the resultant force acting on each nucleus
vanishing. The electrostatic (++) repulsion between the two positive nuclei
is exactly balanced by their attraction to the electrons between them.

1943:Valence
Shell Electron Pair Repulsion (VSEPR) states that electron pairs
(both bonded covalent electron pairs and nonbonded "lone-pairs"
of electrons) repel each other. Methane, CH4, has
four bonded electron pairs and these repel each other to give the four
hydrogens tetrahedral geometry about the central carbon. Likewise, ammonia
has three bonded electron pairs and one lone pair which mutually repel
each other so that ammonia is trigonal pyramidal.

Geometry can be predicted
using the "AXE" system where A is the central atom, X the number of
(electron pair bonded) ligands and E the number of lone pairs.

There are two
VSEPR explorers on the web, The Chemical Thesaurus here
and Cool Molecules here.

The
relationship between VB theory and VSEPR is interesting in that
VSEPR seems to grow out of VB theory.

However,
VB theory is a wave mechanical theory whereas VSEPR assumes that
bonds and lone pairs are entirely classical and says nothing about
how the bonding actually occurs. When moving from VB to VSEPR, it
is as if the wave mechanical electron bonding becomes fixed
in space... in rather like the image on photographic film becomes
fixed during the development process.

There
is no deep theoretical justification to VSEPR theory, other than
it predicts an atomic centre will arrange its ligands so that it
will assume a geometry with the maximum
spherical symmetry. VSEPR theory is "pulled out of a hat",
however, as a method it is very successful.

1960s:Frontier
Molecular Orbital Theory was developed in the 1960s by Kenichi
Fukui who recognised that chemical reactivity can often be explained in
terms of interacting Highest Occupied MOs (HOMOs), Lowest Unoccupied MOs
(LUMOs) and Singly Occupied MOs (SOMOs).

HOMO + LUMO -> bonding MO

HOMO + HOMO -> antibonding
MO

LUMO + LUMO -> null interaction
(no electrons)

SOMO + SOMO -> bonding MO

The FMO approach was developed
by Woodward & Hoffmann in the late nineteen sixties who used it to
explain an apparently diverse set of reactions involving π-systems,
including Diels-Alder cycloaddition, here.
Hoffmann used the approach to explore transition metal complexes.

1941:van Arkel-Ketelaar Triangle recognises three extreme types of
bonding: metallic, ionic and covalent and that many bond types are intermediate
between the extreme types. This behaviour can be rationalised in terms
of electronegativity.

1970s:Molecular
Mechanics and Molecular DynamicsValence Shell
Electron Pair Repulsion (VSEPR) theory has been extensively parameterised
and developed into computer software. The method treats a molecule as
a collection of particles held together by elastic or simple harmonic
forces. These forces can be described in terms of potential energy functions.
The sum of these terms gives the overall steric energy. This system can
be modelled by the Westheimer equation is:

The techniques allows small
molecules such as butane and cyclohexane to be energy minimised into their
most stable conformation:

Larger molecules, including
DNA and proteins can be modelled using MM software. Below is a representation
of bacteriorhodopsin:

In recent years, molecular
mechanics has been extended into molecular dynamics to model large dynamic
structures, such as proteins, with move over a given time scale. Have
a look here (MM)
and here (MD).

Modern Geometry Optimisation
Software uses a variety of techniques: molecular mechanics, semi-empirical,
ab initio (from the beginning) and density functional. The quantum
chemistry software completely hides the mathematics of the geometry optimisation
process. A molecule is constructed (drawn) with a mouse and the energy
minimised using any desired level of theory.

All computational methods uses
a broadly similar strategy. Atoms are placed in virtual space in an approximate
geometry with respect to bond lengths and angles. A calculation is performed
to determine the energy of the system. The software then alters the geometry,
and the energy is recalculated. The software loops, until it finds the
arrangement of nuclei which gives the system the lowest energy, and this
corresponds to the optimum molecular geometry.

The time taken to minimise
depends upon the method used, the size of the molecule, the degree of
precision required and well as the processor speed and available memory.

It is possible to mix-and-match.
An entire protein may be modelled using MM/MD methodology, with the central
active site plus substrate optimised using ab initio techniques.
Software is available from a number of vendors: WaveFunction,
HyperChem(download
a fully functional but time limited demo version) and Gaussian.

The Electron Corral

The image below is not of an
atom, but shows an alternative electron
corral pattern, predicted
by the Schrödinger wave equation and created by electrons in experiment:

The Bifurcation of Theories & Models

The crucial time for understanding [how we understand] chemical structure & bonding occurred in the active UC Beckley labs of G. N. Lewis over the years from 1912–23.

Lewis and colleagues actively debated the new ideas about atomic structure, the Rutherford & Bohr atoms, and postulated how they might give rise to models of chemical structure, bonding & reactivity. Taken directly from the Bohr atom, the Lewis model uses electrons that are "countable dots of negative charge".

Lewis's first ideas about chemical bonding were published in 1916, and later in a more advanced form in 1923. These early ideas have been extensively developed and are now taught to chemistry students the world over.

More advanced models of chemical structure, bonding & reactivity are based upon the Schrödinger equation in which the electron is treated a resonant standing wave.

Although largely outside the scope of this web book, the theoretical dichotomy also occurs in semiconductor physics where electrical behaviour is either modelled in terms of band theory, a natural development of MO theory or in terms of localised electrons & electron holes within the valance band, a development of the VSEPR model.

Classical mechanics represents
atoms as spheres that bond together and exhibit valency. The geometry
of molecules and molecular ions can be very neatly predicted by VSEPR
'theory'. This type of approach can be paramertised into molecular mechanics
and molecular dynamics software models.

The following is taken
from Introduction to Macromolecular Simulation by Peter J.
Steinbach, here:

Quantum chemistry texts can
blur the distinction between quantum mechanics and classical mechanics
and by grouping together LCAO MO calculations along with VSEPR, MM and
MD techniques.

Pick n Mix When
- as chemists - we consider a substance like ammonia, we employ a variety
of models and ideas, fore example:

Bulk property: Ammonia
is a gas at 20°C 1.0 atm, so it is a molecular substance.

In VSEPR theory ammonia,
H3N:, has AX3E trigonal
pyramidal geometry: it is a polar molecule with a lone pair of electrons.

Ammonia is a Lewis base
which complexes with the proton to form the ammonium ion, [NH4]+,
and with Lewis acids such as trialkylboranes, R3B.

The chemistry of ammonia
is dominated by the lone pair of electrons, a model is supported by
the Valence Bond structure.

FMO theory identifies
the HOMO as being the dominant frontier molecular orbital.

Quantum chemistry software
can be used to calculate the geometry of ammonia, in terms of bond lengths
and angles, to high precision. Software can display electron density,
HOMO and LUMO surfaces and calculate infrared spectral bands.

Detailed quantum
analysis shows that ammonia's trigonal pyramidal structure is able
to invert "like an umbrella". In ammonia, this inversion occurs by
quantum
tunnelling.

Can Orbitals be Observed?

One rather important question
remains: Do atomic and molecular orbitals exist? Are they real?

The answer is: No. In
principle orbitals cannot be observed.

Orbitals certainly appear
to exist, and it is often convenient to talk about them as if they
are real, but that is not proof of their actuality.